An imaging mechanism is defined as the process by which a sensor obtains an image of a physical reality. The inversion of the imaging mechanism can be a solution when one needs to measure some physical magnitude from imaging data. In this paper we propose a general method to model and invert such imaging mechanisms. Our approach consists of building a forward model based on the knowledge of the physical properties of the mechanism. Since imaging mechanisms can be nonlinear, we introduce the Volterra series expansion as a tool for the modeling. In order to illustrate our approach, we apply this technique to the estimation of underwater bottom topography using synthetic aperture radar images of the ocean surface.